Abstract
We show that the bulk region reconstructable from a given boundary subregion --- which we term the reconstruction wedge --- can be much smaller than the entanglement wedge even when backreaction is small. We find arbitrarily large separations between the reconstruction and entanglement wedges in near-vacuum states for regions close to an entanglement phase transition, and for more general regions in states with large energy (but very low energy density). Our examples also illustrate situations for which the quantum extremal surface is macroscopically different from the Ryu-Takayanagi surface.
Highlights
Sometimes the gap between approximate and exact quantum error correction is more like a gulf
The Ryu-Takayanagi surface is defined as the minimal area extremal surface homologous to the boundary region A whose area in Planck units gives the CFT entropy of the boundary region A to leading order in the GN expansion
At higher orders in GN, the boundary entropy is no longer given by the area of the RT surface but instead by the generalized entropy associated with the quantum extremal surface [7]
Summary
Sometimes the gap between approximate and exact quantum error correction is more like a gulf. At higher orders in GN, the boundary entropy is no longer given by the area of the RT surface but instead by the generalized entropy associated with the quantum extremal surface [7] This means that the entanglement wedge, defined as the bulk region bounded by the minimal generalized entropy quantum extremal surface, is defined in a state-dependent way. Hayden and Penington [8] first noticed that this state dependence leads to an important modification of the leading order entanglement wedge reconstruction theorems.1 They found that the bulk region that is reconstructable given access only to the boundary region A is not the entanglement wedge, but is instead a potentially much smaller region that depends on the code subspace. We will find a family of simple code subspaces without black holes which exhibit macroscopic gaps between the pure state entanglement wedges and the reconstruction wedge.
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